Carrier Statistics Lab

Calculate the electron & hole density in semiconductors

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Version 2.3 - published on 29 Jul 2014

doi:10.4231/D3K931706 cite this

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    Fermi statistics at different temperature Maxwell-Boltzmann statistics Carrier density during freeze-out Electron density with energy near conduction band



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This is a simple tool that demonstrates electron and hole density distributions based on the Fermi-Dirac and Maxwell Boltzmann equations. This tool shows the dependence of carrier density, densisty of states and occupation factor on temperature and fermi level. User can choose between doped and undoped semi-conductors. Silicon, Germanium, and GaAs can be studied as a function of doping or Fermi level, and temperature.
    Homework: The tool is supported by a homework assignment in which Students are asked to explore the differences between Fermi-Dirac and Maxwell-Boltzmann distributions, compute electron and hole concentrations, study temperature dependences, and study freeze-out.
    First Time User Guide: This document provides important information about the tool, underlying physics and some assignment problems to help the user to get acquainted with the tool.
Bug Fixes:
  • Corrected the display of certain outputs.
Recent upgrades with subsequent versions:
  • 2.1: Added option to add Energy grid and color defined electron/hole plots.
  • 2.0.2: Fixed Si bandgap Si Eg(300K) = 1.1245 eV.
  • 2.0.1: Renamed for Fermi Level and Doping selection. Default setting for doping set to Nd=1e14/cm3 & Na=10/cm3.
  • 2.0: Improved energy grid with inhomogeneous meshing. Temperature dependent electron/hole mass and Bandgap implemented for Si/Ge/GaAs. Plot for Maxwell-Boltzmann statistics updated. Fixed for correct carrier calculation with Fermi-Dirac statistics.
  • 1.2.1: Updated tool tip for correct material parameters being used for simulations.
  • 1.2: Fixed for a bug in calculation of carrier densities. Computed values match analytical results for default input.
  • 1.1: Corrected ni value for Si at 300K. Plots made more resolved in energy axis.
  • 1.03: Updated the Front page of the tool with correct figures of the distributions.
WishList: Detailed information about the wishlist for the tool is here .

Sponsored by



  • Semiconductor Device Fundamentals , Robert Pierret
  • Physics of Semiconductor Devices, S M Sze

Cite this work

Researchers should cite this work as follows:

  • Saumitra Raj Mehrotra, Abhijeet Paul, Gerhard Klimeck (2014), "Carrier Statistics Lab," (DOI: 10.4231/D3K931706).

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